A study on lacunary strong E(r, t)-convergence according to Fk

Abstract

In this manuscript, by using a double band matrix such as Lucas band matrix, a lacunary sequence and a sequence of modulus functions a new generalization is studied in which the concept of lacunary strongE(r,t)-convergence according to F-k is introduced. Then this concept is to be base to createthe sequence space N-theta(E(r,t), F-k), where for instance N-theta(E(r,t), F-k)={x=(x(i)): lim(n ->infinity)1/h(r)Sigma(i is an element of Ir)f(i)(k)E(i)(r,t)(x)-s=0 for somes is an element of C.Furthermore, some inclusion relationships are given on this generalization. Finally, the connectionsbetween the sequence spaces N-theta(E(r,t),F-k) and w(E(r,t),F-k) are investigated